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In this expansion (x-1)(x-2)(x-3)..........(x-18), the coefficient of x^17

In this expansion (x-1)(x-2)(x-3)..........(x-18), the coefficient of x^17

Grade:12th pass

1 Answers

jagdish singh singh
173 Points
7 years ago
\hspace{-0.70 cm}$ writting $(x-1)(x-2)(x-3)\cdots \cdots (x-18)$\\\\\\ $=x^{18}+(1+2+3+\cdots+18)x^{17}+(1\cdot2 +1\cdot 3+\cdots )x^{16}$\\\\\\ So Coeff. of $x^{17} = (1+2+3+\cdots +18)=\frac{1}{2}(18)(19) = 9\cdot 19$

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